arXiv:hep-ph/0405086v3 19 Dec 2005 ∗ eea erhso h Θ by the revived been of chiral have ex- searches pentaquarks the SU(3) several The within the [2]. in predicted model decays first soliton and were masses anti-decuplet the otic and [1], Jaffe of pen- exotic bottomed heptaquark or linear-molecule approach. the in charmed predicted are strange, taquarks new eral antb nepee saqakpu-niur meson quark-plus-antiquark that exotic a numbers first as quantum interpreted the be with be cannot may discovered, they ever mo- because Pentaquarks hadrons effort, compatible channel. this system, Kaon-nucleon tivate - open parity an a with identify only simulations 4,4,4,5,5,5,5,5,5,5,5,5,5,6] In 60]. 59, 58, 57, 56, 55, 54, Θ 53, the lattice 52, of the 51, range the in 50, studied 49, 48, been [47, also have Pen- structures al- pentaquarks. are the taquark scan upgrades further Experimental to out. programmed ready ruled be confirmed, would is for Θ 0 this isospin the If predicting pen- models [46]. pentaquark the 2 theoretical or that the 1 suggests Isospin which have may 33], taquark [32, STAR at recently 6 7 8 9 0 1 2 3,fis icvrda LEPS 25, at 24, discovered Ξ 23, the first 22, of 33], 21, searches 32, 20, recent 31, 19, by 30, 18, and 29, 17, [3], 28, 16, 27, 15, 14, 26, 13, 12, 11, n ES[8 9 0 1 otnet ofimteΘ the confirm to continue 31] Θ new 30, pro- A 29, SVD-2 pentaquark. certain by [28, in experiments, LEPS new produced and recent particular, be that In only show cesses. they can but pentaquarks pentaquarks, the don’t the exclude experiments ex- to positive us ELSA allow the and Nevertheless CLAS previous periments. contradicts positive statis- of higher analysis neg- CLAS number tics of recent the the number example the than For Presently larger experiments. 43]. is 42, experiments 41, ative [40, H1 at and D lcrncades [email protected] address: Electronic ∗− xtcmliursaeepce ic h al works early the since expected are multiquarks Exotic sev- of processes decay and masses the paper this In rdcino h assaddcypoesso tag,cha strange, of processes decay and masses the of Prediction p 30) epcieya A9[4 5 6 7 8 39] 38, 37, 36, 35, [34, NA49 at respectively (3100), ihaynme fsrne hre n otmdqak,are quarks, bottomed and charmed observed. strange, be of still thr number in any crypto-heptaquar assemble possible with quarks The The stability. provides system. con hadron molecular then linear is narrow pair a interaction quark-antiquark additional medium-range An and long-range attraction. in studied The short-range the are repulsive. pentaquarks be Multiquarks ground-state pure In predicted. model. are pentaquarks exotic e.FıiaadCI,IsiuoSpro ´cio v Rov T´ecnico, Av. Superior Instituto CFIF, F´ısica and Dep. etqak rmtelna oeua rpohpaur m crypto-heptaquark molecular linear the from pentaquarks nti ae h assaddcypoesso eea e st new several of processes decay and masses the paper this In .INTRODUCTION I. + xeietlms,qece lattice quenched mass, experimental ++ + etqakwsas discovered also was pentaquark 14)[,4 ,6 ,8 ,10, 9, 8, 7, 6, 5, 4, [3, (1540) −− 16)ado the of and (1860) .Bicudo P. + eos h nryo h utqaksaei computed is state multiquark combina- and the baryons of in the energy decomposed The clusters, colour-singlet mesons. formally simpler be multi- of tions Any can state Hamiltonian. quark (QM) quark-model standard 74]. 73, 72, searches, 71, different [70, any For references with per- see flavours. pentaquarks I of paper of combination this exploration possible In systematic 69]. a [68, form dis- flavours be different presence still several the by may of favoured quarks indeed are heavy pen- Multiquarks two new double-charmed covered. or many one of that with search suggest taquarks [67] expected COMPASS SE- the at at baryons and baryons double-charmed [66], of LEX observation the and reso antd mle hnnra arncdecay hadronic normal than widths. observed smaller two magnitude width, the of decay Importantly, narrow orders extremely baryon. an have three-quark pentaquarks a as or ntepnaursaencsayt ettedifferent the test to necessary data are models. experimental pentaquarks More the with on Kishimoto model, excitation. tri-linear-molecular of quark-antiquark or and 65], a 64, Mateu, [63, hep- Sato and paper, the and this Oset and in applied Llanes-Estrada, 62], Marques, of and [61, PB of excitation model and p-wave anti- taquark Karliner a the Wilczek, and with [2], rota- Jaffe Lipkin field of a model pseudoscalar with diquark the soliton Polyakov triplet in chiral and excitation the Petrov tional are mod- Diakonov, models theoretical of different different model of for Examples room more) still els. (or is five-particle there precision de- states, excellent to an calibrated with properly scribe or accurate are sufficiently physics Be- yet hadronic not non-pertubative pentaquark. of the models of excita- the width. width an cause decay decay nucleon, the propose limits broad a essentially which very tion models and plausible a Kaon all with a Thus resonance in sim- would in it a decay resulting because be and groundstate, cannot recombine the pentaquark in freely state the quark that five known ple well is multiquarks. these It of interpretation the dispute presently ee utqak r tde irsoial na in microscopically studied are multiquarks Here, oevrteosraino the of observation the Moreover models different many that remarkable also is It ∗ arn iheoi etqakflavours, pentaquark exotic with hadrons k iee,adti ssgetdt produce to suggested is this and sidered, eato scmue n ti hw to shown is it and computed is teraction r o xetdt rvd sufficient provide to expected not are s soPi,14-0 iba Portugal Lisboa, 1049-001 Pais, isco irsoial nasadr quark standard a in microscopically ehdoi lses n h central the and clusters, hadronic ee itd eea e xtc may exotics new Several listed. ag,camdadbottomed and charmed range, mdadbottomed and rmed D odel. ∗− p 30)a 1[40] H1 at (3100) 2 with the multiquark matrix element of the QM Hamil- tonian. These matrix elements also produce the short FIG. 1: Examples of overlaps of the Resonant Group Method are depicted, in (a) the norm overlap for the meson-baryon range interaction of the mesonic or baryonic subclusters interaction, in (b) a kinetic overlap for the meson-meson inter- of the multiquark. However, in the case of any pure exotic action, in (c) an interaction overlap for the meson-meson in- groundstate pentaquark, the short-range interaction can teraction, in (d) the annihilation overlap for the meson-baryon be shown to be repulsive [75, 76, 77, 78, 79]. This repul- interaction. These overlaps are simple matrix elements of op- sion agrees with the quenched lattice simulations, which erators with a product of four wave-functions. While the norm in the range of the Θ+ experimental mass, only identify a overlap (a) contributes to the denominators of eqs. (3) and parity - system, compatible with an open Kaon-nucleon (4), the other overlaps (b), (c) and (d) contribute to the ef- channel. fective potential VAB . To search for attraction, one should also study other cluster-cluster interactions. For instance in the N + N Tp ✜ 1 ❭ ✚ 1 ❩ system, the attractive long-range One-Pion-Exchange- (a) ✜ ☛❄p ✄❈ p ✟❭ (b) ✚φ ☛❄p t ✄❈ p ✟φ❩ ✜ 2 ❈ ✄ ✻ ❭ ❩ A 2 ❈ ✄ ✻ A✚ φA φA ❩ ✚ Potential and the medium-range Sigma-Exchange Poten- ❭ ✡❄ ❈ ✄ ✠ ✜ ✏ ✡ ✄❈ ✠ ☛k k ✟✻ ❭ 3 ✄❈ ✜ T1P13 ✄ ❈ ❭ ✡ ✠✜ h i = tial are crucial for the binding of the deuteron. In a hEP14i = E× ✄ ❈ ψ ✚ 3 ✄ ❈ ❩ ✄ ❈ ✚φ ☛❄p p ✟φ❩ microscopic quark Hamiltonian perspective these inter- 4 ✄ ❈ ❩ B 4 ✻ B✚ ✚ ❩ ❩ ✡ ✠✚ ✚φ ☛❄p p ✟φ❩ actions are equivalent to the coupling to a channel with ❩ B 5 ✻ B✚ ✑ 3 ❩ ✡ ✠✚ an extra pion ( S1 quark-antiquark cluster) plus a p-wave ✜ 1 ❭ ✜ ☛❄p ❉ ☎ p ✟❭ 1 ✜φ 2 ❉ ☎ ✻φ ❭ excitation, and to a second channel with two extra s-wave ✚ ❩ (d) A ✡ ✠A (c) ✚φ ☛❄p q ✄❈ p ✟φ❩ ❭ ☛❄ ❉ ☎ ✟ ✜ ❩ A 2 ✻ A✚ k k ✻ pions respectively. Because the long range interaction is ❩ ❈ ✄ ✚ ❭❭ 3 ❉ ☎ ✜✜ ✡ ′ ✄❈ ✠ ✡ ❉❉ ☎☎ ✠ V (p−p ) hA15i = vanishing or small, and the medium range interaction hV13P13i = ✄ ❈ ✄✄r′❈ r❈ may be insufficient to provide all the desired attraction, ✚ 3 ✄ ❈ ❩ ✚ 4 ✄✄A(p−p )❈❈ ❩ ✚φ ☛❄p′ q p′ ✟φ❩ ✚φ ☛❄p′ ✄✄ ❈❈ p′ ✟φ❩ ❩ B 4 ✻ B✚ ❩ B 5 ✄✄ ❈❈ ✻ B✚ the five-quark systems are too unstable to produce nar- ❩ ✡ ✠✚ ❩ ✡ ✠✚ row pentaquarks. Nevertheless, one may consider that an s-wave flavour- singlet light quark-antiquark pair l¯l is added to the pen- old [63, 86]. Assuming this description of the presently taquark M. When the resulting heptaquark M ′ remains observed pentaquarks, I now predict all possible exotic bound, it is a state with parity opposite to the original M strange, charmed and bottomed pentaquarks compatible [80], where the reversed parity occurs due to the intrin- with the linear-molecule model. sic parity of fermions and anti-fermions. The ground- In Section II the exotic baryon-meson short-range s- state of M ′ is also naturally rearranged in an s-wave wave interaction is studied. I find repulsion in ex- baryon and in two s-wave mesons, where the two outer otic multiquarks, and attraction in the channels with hadrons are repelled, while the central hadron provides quark-antiquark annihilation. In Section III the possible stability. The mass of the heptaquark M ′ is expected hadrons with exotic pentaquark flavours are qualitatively to be slightly lower than the exact sum of these stan- studied with an additional quark-antiquark pair. This dard hadron masses due to the binding energy. Because study includes pentaquarks with any number of strange, the s-wave pion is the lightest hadron, the minimum en- charmed and bottomed quarks. I find that several new ergy needed to create a quark-antiquark pair can be as exotics may still be observed. In section IV the conclu- small as 100-200 MeV. This energy shift is lower than the sion is presented. typical energy of 300-600 MeV of spin-isospin or angular excitations in hadrons. Therefore, the first excitation of multiquarks is quark-antiquark creation. Moreover, the II. THE ATTRACTION/REPULSION heptaquarks M ′ may only decay into a low-energy p-wave CRITERION channel (after the extra quark-antiquark pair is annihi- lated), resulting in a very narrow decay width, consistent The standard QM Hamiltonian is, with the observed exotic flavour pentaquarks. The M ′ is then a linear molecular system, light and with a narrow H = Ti + Vij + Ai¯j , (1) width. i iquarkonium to the light pion mass). Moreover, the Resonating Group Method (RGM) [87] was applied TABLE I: Masses and decay processes of exotic flavour pen- taquarks with no heavy quark. The method to arrive at this by Ribeiro, by Oka and Yasaki, and by Toki [88, 89, 90] to table is described in Section III. The possible resonances are show that in exotic N +N scattering the quark two-body- divided in classes characterized by the flavour of light l = u, d potential, together with the Pauli repulsion of quarks, or strange s quarks(antiquarks), and the number or heavy explains the N + N hard core repulsion. Recently, ad- H = c, b quarks(antiquarks). dressing a tetraquark system with π + π quantum num- bers, it was shown that the QM with the quark-antiquark molecule mass [GeV] decay channels ¯ ¯ annihilation Ai¯j also fully complies with chiral symme- I = 1/2, ssssl(+3 ll) : five-hadron molecule try, including the Adler zero and the Weinberg theorem I = 1, sssll¯(+2 ll¯) : four-hadron molecule [91, 92, 93, 94]. I = 3/2, sslll¯(+ll¯)= s¯l • lll • s¯l −− The RGM [87] computes the effective multiquark en- K¯ • N • K¯ = Ξ 1.86 K¯ + Σ, π + Ξ ergy using overlaps, or matrix elements with a larger I = 2, sllll¯(+ll¯)= s¯l • lll • ll¯: pion unbound number of wavefunctions, of the microscopic quark-quark ¯ ¯ ¯• • ¯ interactions. The different examples of overlaps are de- I = 5/2, lllll(+ll)= ll lll ll: pion unbound picted in Fig. 1. Any multiquark state can be formally I = 0, lllls¯(+ll¯)= ls¯ • ll¯• lll decomposed into combinations of simpler colour singlets K • π • N= Θ+ 1.54 K + N clusters, the baryons and mesons. Once the internal en- ergies EA and EB of the two hadronic clusters in the multiquark are accounted for, i. e. , quark-antiquark annihilation potential Ai¯j is also con- p strained when the quark model produces spontaneous hφB φA|H (−1) P |φAφB i p chiral-symmetry breaking [96]. The annihilation poten- p = EA + EB + VA B , (3) hφB φA| Pp(−1) P |φAφB i tial A is present in the π Salpeter equation, where (P−1)pP is the antisymmetrizer, the remaining p 2T + V A φ+ φ+ energy of the multiquark is the effective hadron-hadron = Mπ , (6) P A 2T + V φ− −φ− potential VA B. The meson-baryon or meson-meson po- " # ! ! tential is computed with the overlap of the inter-cluster microscopic potentials where the π is the only hadron with a large negative- energy wavefunction, φ− ≃ φ+. In eq. (6) the annihila- V bar A = hφB φA|− (V14 + V15 +2V24 +2V25)3P14 tion potential A cancels most of the kinetic energy and mes B confining potential 2T + V . This is the reason why the pion has a very small mass. From the hadron spectrum +3A15|φAφB i/hφB φA|1 − 3P14|φAφB i and using eq. (6), the matrix elements of the annihilation V mes A = hφB φA|(1 + PAB)[−(V13 + V23 + V14 + V24) mes B potential are determined as, ×P13 + A23 + A14]|φAφB i 2 h2T + V iS=0 ≃ (2MN − M∆) /hφB φA|(1 + PAB )(1 − P13)|φAφBi , (4) 3 2 where Pij stands for the exchange of particle i with par- ⇒ hAi =0 ≃ − (2M − M∆) , (7) S 3 N ticle j, see Fig. 1. Actually, VA B only corresponds to the short range interaction of the hadrons A and B. which is correct for the annihilation of u or d quarks, and For the purpose of this paper the details of the po- nearly correct for the s quark. tentials in eq. (1) are unimportant, only their matrix The annihilation potential only shows up in non-exotic elements matter, because the effective hadron-hadron in- channels, and it is clear from eq. (7) that the annihila- teraction can be decomposed in RGM overlaps. The over- tion potential provides an attractive (negative) interac- laps are similar to the matrix elements occuring in the tion. The quark-quark(antiquark) potential is dominated variational method fo the Schr¨odinger equation, where by the interplay of the hyperfine interaction of eq. (5) the product of two wavefunctions is replaced by a prod- and the quark exchange of eq. (4). In s-wave systems uct of four wavefunctions. For example the RGM overlap with low spin this results in a repulsive interaction. The (c) of Fig. 1 is identical to the matrix element of the hy- short-range interactions are independent of the details perfine potential times an algebraic number and a factor of the chiral-invariant quark model that one chooses to with the dimension of the square of the wave-function. consider. Therefore, I arrive at the attraction/repulsion The hadron spectrum constrains the matrix element of criterion for groundstate hadrons: the hyperfine potential - whenever the two interacting hadrons have quarks (or 4 antiquarks) with a common flavour, the repulsion is in- hVhypi≃ (M∆ − MN ) ≃ MK∗ − MK . (5) creased by the Pauli principle; 3 - when the two interacting hadrons have a quark and an When a light quark is replaced by a heavy quark [95], it antiquark with the same flavour, the attraction is en- ∗ must also be replaced by hVhypDi ≃ MD − MD. The hanced by the quark-antiquark annihilation. 4

TABLE II: Masses and decay processes of exotic flavour pen- TABLE III: Masses and decay processes of exotic flavour taquarks with one heavy quark. The method to arrive at this pentaquarks with one heavy anti-quark. The method to ar- table is described in Section III. The possible resonances are rive at this table is described in Section III. The possible divided in classes characterized by the flavour of light l = u, d resonances are divided in classes characterized by the flavour or strange s quarks (antiquarks), and the number or heavy of light l = u, d or strange s quarks (antiquarks), and the H = c, b quarks (antiquarks). number or heavy H = c, b quarks (antiquarks). linear molecule mass [GeV] decay channels linear molecule mass [GeV] decay channels I = 1/2,Hsss¯l(+2 ll¯) : four-hadron molecule I = 0, ssssH¯ (+3ll¯) : five-hadron molecule I = 1,Hssll¯(+ll¯)= s¯l • llH • s¯l I = 1/2, ssslH¯ (+2 ll¯) : four-hadron molecule K¯ • Λc • K¯ 3.23 ± 0.03 K¯ + Ξc, π + Ωc I = 0, ssllH¯ (+ll¯)= lH¯ • ll¯• lss K¯ • Λb • K¯ 6.57 ± 0.03 K¯ + Ξb, π + Ωb D¯ • π • Ξ 3.31 ± 0.03 D¯ + Ξ, D¯ s + Λ ∗ ∗ ∗ I = 3/2,Hslll¯(+ll¯)= s¯l • lll • H¯l D¯ • π • Ξ 3.45 ± 0.03 D¯ + Ξ, D¯ s + Λ, D¯ s + Λ K¯ • N • D 3.25 ± 0.03 K¯ + Σc, D + Σ, π + Ξc B • π • Ξ 6.73 ± 0.03 B + Ξ, Bs + Λ ∗ ∗ ∗ ∗ ∗ K¯ • N • D 3.39 ± 0.03 K¯ + Σc, D + Σ, π + Ξc B • π • Ξ 6.77 ± 0.03 B + Ξ, Bs + Λ, Bs + Λ K¯ • N • B¯ 6.66 ± 0.03 K¯ + Σb, B¯ + Σ, π + Ξb I = 1/2, slllH¯ (+ll¯)= lH¯ • ll¯• lls ∗ ∗ K¯ • N • B¯ 6.71 ± 0.03 K¯ + Σb, B¯ + Σ, π + Ξb D¯ • π • Σ 3.19 ± 0.03 D¯ + Λ, D¯ + Σ, D¯ s + N ∗ ∗ ∗ ∗ I = 2,Hllll¯(+ll¯)= ll¯• lll • H¯l : pion unbound D¯ • π • Σ 3.33 ± 0.03 D¯ + Λ, D¯ + Σ, D¯ s + N I = 1/2,Hllls¯(+ll¯)= ls¯ • ll¯• llH B • π • Σ 6.60 ± 0.03 B + Λ, B + Σ, Bs + N ∗ ∗ ∗ ∗ K • π • Σc 3.08 ± 0.03 K + Λc, K + Σc, Ds + N B • π • Σ 6.64 ± 0.03 B + Λ, B + Σ, Bs + N K • π • Σb 6.41 ± 0.1 K + Λb, K + Σb, Ds + N I = 1/2, slllH¯ (+ll¯)= lH¯ • s¯l • lll I = 1/2,Hllls¯(+ll¯)= ls¯ • H¯l • lll D¯ • K¯ • N 3.25 ± 0.03 D¯ + Λ, D¯ + Σ, D¯ s + N ∗ ∗ ∗ ∗ K • D • N 3.25 ± 0.03 K + Λc, K + Σc, Ds + N D¯ • K¯ • N 3.39 ± 0.03 D¯ + Λ, D¯ + Σ, D¯ s + N ∗ ∗ K • D • N 3.39 ± 0.03 K + Λc, K + Σc, Ds + N B • K¯ • N 6.66 ± 0.03 B + Λ, B + Σ, Bs + N ∗ ∗ ∗ ∗ K • B¯ • N 6.66 ± 0.03 K + Λb, K + Σb, B¯s + N B • K¯ • N 6.71 ± 0.03 B + Λ, B + Σ, Bs + N ∗ ∗ K • B¯ • N 6.71 ± 0.03 K + Λb, K + Σb, B¯s + N I = 0, llllH¯ (+ll¯)= lH¯ • ll¯• lll D¯ • π • N 2.93 ± 0.03 D¯ + N ∗ ∗− ∗ D¯ • π • N= D¯ p 3.10 D¯ + N, D¯ + N For instance, uud − su¯ is attractive, and uud − us¯ is B • π • N 6.35 ± 0.03 B + N ∗ ∗ repulsive. In the cases where attraction is added to repul- B • π • N 6.39 ± 0.03 B + N, B + N sion, it turns out that attraction prevails when there are more quark-antiquark matchings than quark-quark ones. For example, uus − su¯ is attractive whereas uss − su¯ is repulsive. This qualitative rule is confirmed by quantita- minimally exotic isospin, and with low spin. tive computations of the short-range interactions of the b) Here the flavour is decomposed in an s-wave system of π, N, K, D, D∗,B,B∗ [63, 81, 82, 86, 91, 92, 94]. This a spin 1/2 baryon and two pseudoscalar mesons, except ∗ ∗ rule can also be applied to other baryons. I find for ex- for the vectors D and B which are also considered. ample that the π • Λ short-range interaction is vanishing, c) I only consider, as candidates for narrow pentaquarks, while the I =3/2, K¯ • Σ interaction is repulsive. the systems where at least one hadron is attracted by both other ones. The attraction/repulsion criterion is used to discriminate which hadrons are bound and which are repelled. III. EXOTIC-FLAVOUR PENTAQUARKS d) In the case of some exotic flavour pentaquarks, only a four-hadron-molecule or a five-hadron-molecule would The exotic pentaquarks containing five quarks only are bind. These cases are not detailed in the tables, because not expected to bind, due to the attraction/repulsion cri- they are difficult to create in the laboratory. terion. To increase binding we include a light l¯l quark- e) Moreover, in the particular case where one of the three antiquark pair in the system. I now detail the strategy hadrons is a π, binding is only assumed if the π is the to find the possible linear heptaquark molecules. central hadron, attracted both by the other two ones. a) I consider any heptaquark with the flavour of an exotic The π is too light to be bound by just one hadron [63]. pentaquark and with up to two heavy flavours or anti- f) The masses of the bound states with a pion are com- flavours. Hadrons with three heavy flavour are presently puted assuming a total binding energy of the order of quite hard to produce in the laboratory. The top quark 10 MeV, averaging the binding energy of the Θ+ and is excluded because it is too unstable. To minimise the of the D∗−p system in the molecular perspective. The short-range repulsion and to increase the attraction of the masses of the other bound states are computed assuming three-hadron system, I only consider pentaquarks with a a total binding energy of the order of 50 MeV, averaging 5

TABLE IV: Masses and decay processes of exotic flavour TABLE V: Masses and decay processes of exotic flavour pen- pentaquarks with two heavy quarks. The method to arrive at taquarks with one heavy quark and one heavy anti-quark. this table is described in Section III. The possible resonances The method to arrive at this table is described in Section III. are divided in classes characterized by the flavour of light The possible resonances are divided in classes characterized by l = u, d or strange s quarks (antiquarks), and the number or the flavour of light l = u, d or strange s quarks (antiquarks), heavy H = c, b quarks (antiquarks). and the number or heavy H = c, b quarks (antiquarks).

linear molecule mass [GeV] decay channels linear molecule mass [GeV] decay channels ′ I = 1/2, HHss¯l(+ll¯)= H¯l • lss • H¯l I = 0,HsssH¯ (+2 ll¯) : four-hadron molecule ′ ′ D • Ξ • D 5.00 ± 0.03 D + Ωc, K¯ + Ωcc I = 1/2,HsslH¯ (+ll¯)= lss • H¯l • lH¯ ∗ ∗ ∗ ∗ ∗ D • Ξ • D 5.14 ± 0.03 D(D ) + Ωc, K¯ + Ωcc Ξ • D¯ • B¯(B¯ ) 8.41 (8.46) ± 0.03 Ξ+ B¯c(B¯c ), Ωc + B¯(B¯ ) ∗ ∗ ∗ ∗ ∗ ∗ ∗ D • Ξ • D 5.29 ± 0.03 D + Ωc, K¯ + Ωcc Ξ • D¯ • B¯(B¯ ) 8.55 (8.60) ± 0.03 Ξ+ B¯c(B¯c ), Ωc + B¯(B¯ ) ∗ ∗ ∗ ∗ D • Ξ • B¯(B¯ ) 8.41 (8.46) ± 0.03 D + Ωb, B¯(B¯ ) + Ωc Ξ • B(B¯ ) • D 8.41 (8.46) ± 0.03 Ξ+ Bc(B¯c ), Ωb + D ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ D • Ξ • B¯(B¯ ) 8.56 (8.60) ± 0.03 D + Ωb, B¯(B¯ ) + Ωc Ξ • B(B¯ ) • D 8.55(8.60) ± 0.03 Ξ+ Bc(B¯c ), Ωb + D ∗ ∗ ′ ′ B¯ • Ξ • B¯(B¯ ) 11.83(11.87) ± 0.03 B¯(B¯ ) + Ωb, K¯ + Ωbb I = 0,HsllH¯ (+ll¯)= llH • s¯l • lH¯ ∗ ∗ ∗ ∗ ∗ ∗ B¯ • Ξ • B¯(B¯ ) 11.87(11.92) ± 0.03 B¯(B¯ ) + Ωb, K¯ + Ωbb Λb • K¯ • D¯(D¯ ) 7.94(8.08) ± 0.1 Ξb + D¯ (D ), Λb + D¯ s(D¯ s ) ∗ ∗ ∗ I = 1/2, HHss¯l(+ll¯)= s¯l • lHH • s¯l Λc • K¯ • B(B ) 8.01(8.06) ± 0.03 Ξc + B(B ), Λc + Bs(Bs ) ′ ′ K¯ • Ξcc • K¯ 4.52 ± 0.1 K¯ + Ωcc, D + Ωc I = 0,HsllH¯ (+ll¯)= lls • H¯l • lH¯ ¯ ¯ ¯ ∗ ∗ ∗ K • Ξcb(Ξbb) • K 7.77 (11.02) ± 0.1 K + Ωcb(Ωbb), D + Ωb Λ • D • B(B ) 8.21(8.26) ± 0.03 Ξc + B(B ), Λ+ Bd(Bd ) ∗ ∗ ∗ ∗ I = 1, HHsll¯(+ll¯)= H¯l • lls • H¯l Λ • D • B(B ) 8.35(8.40) ± 0.03 Ξc + B(B ), Λ+ Bd(Bd ) ∗ ∗ D • Λ • D 4.80 ± 0.03 D + Ξc, K¯ + Ξcc, π + Ωcc Λ • B¯(B¯ ) • D¯ 8.21(8.26) ± 0.03 Ξb + D,¯ Λ+ D¯ b(D¯ b ) ∗ ∗ ∗ ∗ ∗ ∗ D • Λ • D 4.94 ± 0.03 D(D ) + Ξc, K¯ + Ξcc Λ • B¯(B¯ ) • D¯ 8.35(8.40) ± 0.03 Ξb + D¯ , Λ+ D¯ b(D¯ b ) ∗ ∗ ∗ ′ ′ D • Λ • D 5.08 ± 0.03 D + Ξc, K¯ + Ξcc I = 1/2,HlllH¯ (+ll¯)= llH • ll¯• lH¯ ∗ ∗ ∗ ∗ D • Λ • B¯(B¯ ) 8.21(8.26) ± 0.03 D + Ξb, B¯(B¯ ) + Ξc Σc • π • B(B ) 7.86 (7.91) ± 0.03 Λc(Σc)+ B(B ), N + Bd ∗ ∗ ∗ ∗ ∗ ∗ D • Λ • B¯(B¯ ) 8.35(8.40) ± 0.03 D + Ξb, B¯(B¯ ) + Ξc Σb • π • D¯(D¯ ) 7.78(7.92) ± 0.1 Λb(Σb)+ D¯(D¯ ), N + B¯c ∗ ∗ ′ ′ B¯ • Λ • B¯(B¯ ) 11.62(11.67) ± 0.03 B¯(B¯ ) + Ξb, K¯ + Ξbb I = 1/2,HlllH¯ (+ll¯)= lll • H¯l • lH¯ ¯∗ ¯ ¯∗ ¯ ¯∗ ¯ ∗ ∗ ∗ B • Λ • B(B ) 11.67(11.72) ± 0.03 B(B ) + Ξb, K + Ξbb N • D • B(B ) 8.04 (8.08) ± 0.03 Λc + B(B ), N + Bd(Bd ) ¯ ¯ ¯ ¯ ∗ ∗ ∗ ∗ I = 1, HHsll(+ll)= Hl • llH • sl N • D • B(B¯ ) 8.18 (8.22) ± 0.03 Λc + B(B ), N + Bd (Bd) ∗ ∗ ∗ ∗ B¯(B¯ ) • Λc • K¯ 8.01(8.06) ± 0.03 B¯(B¯ ) + Ξc, Ξcb + K¯ N • B¯(B¯ ) • D¯ 8.04 (8.08) ± 0.03 Λb + D,¯ N + B¯c(B¯c ) ∗ ∗ ∗ ∗ ∗ ∗ D(D ) • Λb • K¯ 7.94(8.08) ± 0.1 D(D ) + Ξb, Ξcb + K¯ N • B¯(B¯ ) • D¯ 8.18 (8.22) ± 0.03 Λb + D¯ , N +(B¯c)B¯c I = 3/2, HHlll¯(+ll¯)= H¯l • lll • H¯l D • N • D 4.62 ± 0.03 D + Σc, π + Ξcc ∗ ∗ D • N • D 4.76 ± 0.03 D + Σc, D + Σc ∗ • • ∗ ± ∗ bar of ± 30 MeV for the mass of the multiquark. When D N D 4.91 0.03 D + Σc, π + Ξcc one of the hadrons in the molecule is not listed by the • • ¯ ¯∗ ± ¯ ¯∗ D N B(B ) 8.04 (8.08) 0.03 D + Σb, B(B ) + Σc Particle Data Group [97], the hadron mass is extracted ∗ ∗ ∗ ∗ D • N • B¯(B¯ ) 8.18 (8.22) ± 0.03 D + Σb, B¯(B¯ ) + Σc from a recent lattice computation [98], and the error bar ∗ ∗ B¯ • N • B¯(B¯ ) 11.45 (11.49) ± 0.03 B¯(B¯ ) + Σb, π + Ξbb for the mass of the multiquark is ± 100 MeV. ∗ ∗ ∗ B¯ • N • B¯(B¯ ) 11.49 (11.54) ± 0.03 B¯(B¯ ) + Σb, π + Ξbb h) Although three-body decay channels are possible I = 0, HHlls¯(+ll¯)= ls¯ • ll¯• lHH through quark rearrangement, their observation requires K • π • Ξcc 4.20 ± 0.1 K + Ξcc, Ds + Λc high experimental statistics. Only some of the different possible two-body decay processes are detailed here. K • π • Ξcb(Ξbb) 7.45 (10.70) ± 0.1 K + Ξcb(Ξbb), Ds + Λc I = 0, HHlls¯(+ll¯)= ls¯ • H¯l • llH The possible narrow exotic-flavour pentaquarks are ∗ ∗ summarised in Tables I, II, III, IV and V. For each K • D(D ) • Λb 8.01(8.06) ± 0.1 K + Ξcb, Ds(Ds ) + Λb • ¯ ¯∗ • ± ¯ ¯∗ flavour the heptaquark structure is produced, and the K B(B ) Λc 7.94(8.08) 0.03 K + Ξcb, Bs(Bs ) + Λc possible molecular states are listed together with the pos- sible two-body decay processes. Three-body decays may also be possible, but they are not detailed here. For the binding energies of the Ξ−− and of the new positive- isospin I 6= 0 the decay processes are shown in a con- −− parity DS mesons. densed form. For instance, the Ξ observed at NA49 g) For a more precise binding energy one would need [34] belongs to an iso-quadruplet, and in Table I the decay to include the attractive medium-range interaction, the process is summarised into K¯ +Σ, where K corresponds full three-body Fadeev effects, and the coupling to p- to either K+ or to K0 while K¯ corresponds either to K− wave decay channels. Nevertheless all these effects should or K¯ 0. When the isospin is specified, the different mem- increase the binding energy, without changing the hep- bers of the quadruplet decay respectively to K− + Ξ−, taquark picture of this paper. This results in an error to K− + Ξ0 and K¯ 0 + Ξ−, to K− + Ξ+ and K¯ 0 + Ξ0, 6 and to K¯ 0 + Ξ+. Moreover, Tables IV and V have a very candidates are the I =1/2, slll¯(+ l¯l)c = N • K¯ • D and ¯ ∗ large number of states, and therefore these tables are fur- slll(+l¯l)c = N •K¯ •D states. Notice that the Ds(2317) ther condensed when at least one of the heavy quarks is might be a I = 0, K¯ • D state, the Ds(2460) might be a bottom quark. For instance, B(B∗) means that both a I = 0, K¯ • D∗ state with 60 MeV binding energies, B and B∗ states should be considered. [82, 83, 84, 85], and that the Λ(1405) may also be a I = 0, N • K¯ with binding energy of 30 MeV (mixed with a Σ • π state) [99, 100]. This particular pentaquark IV. CONCLUSION AND OUTLOOK candidate is thus expected to have a large binding energy, of the order of 100 MeV, possibly larger than the binding This work has performed a systematic search of energy of the other resonances of its class. Moreover the ∗ exotic-flavour pentaquarks, using the linear three-body π, the K¯ , the N and the D can be detected by most hadronic-molecule perspective. This perspective is the experimental collaborations. Thus these two resonances, result of standard QM computations of pentaquarks with masses of the order of respectively 3.20 to 3.25 Gev masses and of hadron-hadron short-range interactions. and 3.34 to 3.39 GeV, decaying into the two-body decays This view, where the quark-antiquark annihilation is cru- listed in Table III and also in three-body decays, say in ∗ cial, explains the difficulty of quenched lattice QCD com- D¯(D¯ ) + π + Σ are excellent candidates for new pen- putations in identifying the positive parity pentaquark taquarks. If one of these new resonances is observed, it 0+. I only consider pentaquarks with an extra light l¯l will provide an excellent evidence for hadronic molecules. quark-antiquark pair (total parity +), minimal exotic The quantitative computation of the masses, decay isospin, and spin 1/2. These are the most favourable rates and sizes of some of the proposed heptaquarks will conditions to have exotic pentaquarks, but nevertheless be done elsewhere. The most relevant contributions that more exotic states may still be observed. Because quark remain to be included in this framework are the attractive models are not fully calibrated yet, the results are af- medium-range interaction, the full three-body Fadeev ef- fected by an error bar. fects, and the coupling to p-wave decay channels. A large number of new exotic flavour-pentaquarks are Acknowledgments predicted in Tables I, II, III, IV and V, together with their decay channels. It is interesting to remark that degenerate states occur in Tables II and IV, and in Tables I am grateful to Katerina Lipka, Achim Geiser, Paula III and V. Bordalo and Pedro Abreu for discussions on the possi- Moreover, some new multiquarks are easier to bind bility to detect new exotic pentaquarks. This work is than the presently observed exotic pentaquarks. In par- devoted to encourage the experimental search for new ticular two very promising new exotic-flavour pentaquark exotic multiquarks.

[1] R.L. Jaffe, SLAC-PUB-1774, talk presented at the Topi- arXiv:hep-ex/0401024. cal Conf. on Baryon Resonances, Oxford, England, July [12] J. Z. Bai et al. [BES Collaboration], 5-9, 1976; R. L. Jaffe, Phys. Rev. D 15 281 (1977). arXiv:hep-ex/0402012. [2] D. Diakonov, V. Petrov and M. V. Polyakov, Z. Phys. [13] M. Abdel-Bary et al. [COSY-TOF Collaboration], A 359 305 (1997) [arXiv:hep-ph/9703373]. arXiv:hep-ex/0403011. [3] T. Nakano et al. [LEPS Collaboration], Phys. Rev. Lett. [14] K. T. Knopfle, M. Zavertyaev and T. Zivko [HERA-B 91, 012002 (2003) [arXiv:hep-ex/0301020]. Collaboration], arXiv:hep-ex/0403020. [4] V. V. Barmin et al. [DIANA Collaboration], Phys. [15] P. Z. Aslanyan, V. N. Emelyanenko and Atom. Nucl. 66, 1715 (2003) [Yad. Fiz. 66, 1763 (2003)] G. G. Rikhkvitzkaya, arXiv:hep-ex/0403044. [arXiv:hep-ex/0304040]. [16] S. Chekanov et al. [ZEUS Collaboration], [5] S. Stepanyan et al. [CLAS Collaboration], Phys. Rev. arXiv:hep-ex/0403051. Lett. 91, 252001 (2003) [arXiv:hep-ex/0307018]. [17] C. Pinkenburg, arXiv:nucl-ex/0404001. [6] J. Barth et al. [SAPHIR Collaboration], [18] Y. A. Troyan, A. V. Beljaev, A. Y. Troyan, arXiv:hep-ex/0307083. E. B. Plekhanov, A. P. Jerusalimov, G. B. Piskaleva [7] A. E. Asratyan, A. G. Dolgolenko and M. A. Kubantsev, and S. G. Arakelian, arXiv:hep-ex/0404003. arXiv:hep-ex/0309042. [19] S. Raducci, P. Abreu, A. De Angelis, DELPHI note [8] V. Kubarovsky et al. [CLAS Collaboration], Phys. Rev. 2004-002 CONF 683, March 2004. Lett. 92, 032001 (2004) [Erratum-ibid. 92, 049902 [20] Y. M. Antipov et al. [SPHINX Collaboration], Eur. (2004)] [arXiv:hep-ex/0311046]. Phys. J. A 21, 455 (2004) [arXiv:hep-ex/0407026]. [9] A. Airapetian et al. [HERMES Collaboration], Phys. [21] I. Abt et al. [HERA-B Collaboration], Phys. Rev. Lett. Lett. B 585, 213 (2004) [arXiv:hep-ex/0312044]. 93, 212003 (2004) [arXiv:hep-ex/0408048]. [10] H. G. Juengst [CLAS Collaboration], [22] M. J. Longo et al. [HyperCP Collaboration], Phys. Rev. arXiv:nucl-ex/0312019. D 70, 111101 (2004) [arXiv:hep-ex/0410027]. [11] A. Aleev et al. [SVD Collaboration], [23] B. Aubert et al. [BABAR Collaboration], Phys. Rev. 7

Lett. 95, 042002 (2005) [arXiv:hep-ex/0502004]. and H. Suganuma, Nucl. Phys. A 755, 467 (2005) [24] M. Z. Wang et al., Phys. Lett. B 617, 141 (2005) [arXiv:hep-lat/0501022]. [arXiv:hep-ex/0503047]. [57] B. G. Lasscock et al., Phys. Rev. D 72, 014502 (2005) [25] P. Z. Aslanyan, V. N. Emelyanenko and [arXiv:hep-lat/0503008]. G. G. Rikhkvitzkaya, arXiv:hep-ex/0504026. [58] T. T. Takahashi, T. Umeda, T. Onogi and [26] K. H. Hicks, Prog. Part. Nucl. Phys. 55, 647 (2005) T. Kunihiro, Phys. Rev. D 71, 114509 (2005) [arXiv:hep-ex/0504027]. [arXiv:hep-lat/0503019]. [27] M. Battaglieri et al. [CLAS Collaboration], [59] N. Ishii, T. Doi, Y. Nemoto, M. Oka and arXiv:hep-ex/0510061. H. Suganuma, Phys. Rev. D 72, 074503 (2005) [28] A. Aleev et al. [SVD Collaboration], [arXiv:hep-lat/0506022]. arXiv:hep-ex/0401024. [60] S. Basak et al., Phys. Rev. D 72, 094506 (2005) [29] A. Aleev et al. [SVD Collaboration], [arXiv:hep-lat/0506029]. arXiv:hep-ex/0509033. [61] R. L. Jaffe and F. Wilczek, Phys. Rev. Lett. 91, 232003 [30] A. Kubarovsky and V. Popov [SVD Collaboration], (2003) [arXiv:hep-ph/0307341]. arXiv:hep-ex/0510006. [62] M. Karliner and H. J. Lipkin, arXiv:hep-ph/0307243. [31] T. Nakano, Talk presented at Pentaquark05, Jefferson [63] P. Bicudo and G. M. Marques, Phys. Rev. D 69, 011503 Lab. (2004) [arXiv:hep-ph/0308073]. [32] S. Kabana [STAR Collaboration], Acta Phys. Hung. A [64] F. J. Llanes-Estrada, E. Oset and V. Mateu, 24, 321 (2005) [arXiv:hep-ex/0406032]. arXiv:nucl-th/0311020. [33] H. Z. Huang, arXiv:nucl-ex/0509037. [65] T. Kishimoto and T. Sato, arXiv:hep-ex/0312003. [34] C. Alt et al. [NA49 Collaboration], Phys. Rev. Lett. 92, [66] M. Mattson et al. [SELEX Collaboration], Phys. Rev. 042003 (2004) [arXiv:hep-ex/0310014]. Lett. 89, 112001 (2002) [arXiv:hep-ex/0208014]. [35] H. G. Fischer and S. Wenig, arXiv:hep-ex/0401014. [67] L. Schmitt, S. Paul, R. Kuhn and M. A. Moinester, [36] J. W. Price, J. Ducote, J. Goetz and B. M. K. Nefkens arXiv:hep-ex/0310049. [CLAS Collaboration], arXiv:nucl-ex/0402006. [68] J. M. Richard, arXiv:hep-ph/0212224. [37] A. Airapetian et al. [HERMES Collaboration], Phys. [69] M. F. M. Lutz and E. E. Kolomeitsev, Rev. D 71, 032004 (2005) [arXiv:hep-ex/0412027]. arXiv:nucl-th/0402084. [38] S. Chekanov et al. [ZEUS Collaboration], Phys. Lett. B [70] S. L. Zhu, Phys. Rev. C 70, 045201 (2004) 610, 212 (2005) [arXiv:hep-ex/0501069]. [arXiv:hep-ph/0405149]. [39] D. C. Christian et al. [E690 Collaboration], Phys. Rev. [71] S. L. Zhu, Int. J. Mod. Phys. A 19, 3439 (2004) Lett. 95, 152001 (2005) [arXiv:hep-ex/0507056]. [arXiv:hep-ph/0406204]. [40] [H1 Collaboration], arXiv:hep-ex/0403017. [72] W. Roberts, Phys. Rev. C 70, 065201 (2004) [41] S. Chekanov et al. [ZEUS Collaboration], Eur. Phys. J. [arXiv:nucl-th/0408034]. C 38, 29 (2004) [arXiv:hep-ex/0409033]. [73] X. R. Lu, Y. J. Mao and B. Q. Ma, High Energy Phys. [42] M. Zavertyaev, arXiv:hep-ex/0501028. Nucl. Phys. 29, 210 (2005). [43] J. M. Link et al. [FOCUS Collaboration], Phys. Lett. B [74] X. G. He, X. Q. Li, X. Liu and X. Q. Zeng, Eur. Phys. 622, 229 (2005) [arXiv:hep-ex/0506013]. J. C 44, 419 (2005) [Erratum-ibid. C 44, 459 (2005)] [44] M. Ablikim et al. [BES Collaboration], [arXiv:hep-ph/0502236]. arXiv:hep-ex/0405030. [75] P. Bicudo and J. E. Ribeiro, Z. Phys. C 38, 453 (1988). [45] I. G. Alekseev et al. [EPECUR Collaboration], [76] P. Bicudo, J. E. Ribeiro and J. Rodrigues, Phys. Rev. arXiv:hep-ex/0509032. C 52, 2144 (1995). [46] S. Capstick, P. R. Page and W. Roberts, Phys. Lett. B [77] I. Bender, H. G. Dosch, H. J. Pirner and H. G. Kruse, 570, 185 (2003) [arXiv:hep-ph/0307019]. Nucl. Phys. A 414, 359 (1984). [47] Y. Nemoto, N. Nakajima, H. Matsufuru and [78] T. Barnes and E. Swanson, Phys. Rev. C 49 1166 H. Suganuma, Phys. Rev. D 68, 094505 (2003) (1994). [arXiv:hep-lat/0302013]. [79] J. S. Hyslop, R. A. Arndt, L. D. Roper and R. L. Work- [48] F. Csikor, Z. Fodor, S. D. Katz and T. G. Kovacs, JHEP man, Phys. Rev. D 46 961 (1992). 0311, 070 (2003) [arXiv:hep-lat/0309090]. [80] M. A. Nowak, M. Rho and I. Zahed, Phys. Rev. D 48, [49] S. Sasaki, Phys. Rev. Lett. 93, 152001 (2004) 4370 (1993) [arXiv:hep-ph/9209272]. [arXiv:hep-lat/0310014]. [81] P. Bicudo, Phys. Rev. D 70, 111504 (2004) [50] T. W. Chiu and T. H. Hsieh, Phys. Rev. D 72, 034505 [arXiv:hep-ph/0403146]. (2005) [arXiv:hep-ph/0403020]. [82] P. Bicudo, Nucl. Phys. A 748, 537 (2005) [51] T. Doi, N. Ishii, M. Oka and H. Suganuma, Phys. Rev. [arXiv:hep-ph/0401106]. D 70, 034510 (2004) [arXiv:hep-lat/0402005]. [83] T. Barnes, F. E. Close and H. J. Lipkin, Phys. Rev. D [52] F. Okiharu, H. Suganuma and T. T. Takahashi, Phys. 68, 054006 (2003) [arXiv:hep-ph/0305025]. Rev. Lett. 94, 192001 (2005) [arXiv:hep-lat/0407001]. [84] K. Terasaki, Phys. Rev. D 68, 011501 (2003) [53] C. Alexandrou and G. Koutsou, Phys. Rev. D 71, [arXiv:hep-ph/0305213]. 014504 (2005) [arXiv:hep-lat/0407005]. [85] K. Terasaki and B. H. J. McKellar, Prog. Theor. Phys. [54] N. Ishii, T. Doi, H. Iida, M. Oka, F. Okiharu 114, 205 (2005) [arXiv:hep-ph/0501188]. and H. Suganuma, Phys. Rev. D 71, 034001 (2005) [86] P. Bicudo, Phys. Rev. D 71 (2005) 011501 [arXiv:hep-lat/0408030]. [arXiv:hep-ph/0403295]. [55] F. Okiharu, H. Suganuma and T. T. Takahashi, Phys. [87] J. Wheeler, Phys. Rev. 52, 1083 (1937); ibidem 1107. Rev. D 72, 014505 (2005) [arXiv:hep-lat/0412012]. [88] J. E. Ribeiro, Z. Phys. C 5, 27 (1980). [56] N. Ishii, T. Doi, H. Iida, M. Oka, F. Okiharu [89] M. Oka and K. Yazaki, Prog. Theor. Phys. Phys. Lett. 8

B90 (1980) 41; Prog. Theor. Phys. 66 (1981) 556, 572. [96] P. Bicudo and J. E. Ribeiro, Phys. Rev. D 42, 1611 [90] H. Toki, Z. Phys. A294 (1980) 173. (1990); ibidem D 42, 1625; ibidem D 42, 1635. [91] P. Bicudo, Phys. Rev. C 67, 035201 (2003). [97] K. Hagiwara et al. [Particle Data Group Collaboration], [92] P. Bicudo, S. Cotanch, F. Llanes-Estrada, P. Maris, Phys. Rev. D 66, 010001 (2002). J. E. Ribeiro and A. Szczepaniak, Phys. Rev. D 65, [98] N. Mathur, R. Lewis and R. M. Woloshyn, Phys. Rev. 076008 (2002) [arXiv:hep-ph/0112015]. D 66, 014502 (2002) [arXiv:hep-ph/0203253]. [93] F. J. Llanes-Estrada and P. De A. Bicudo, Phys. Rev. [99] D. Jido, J. A. Oller, E. Oset, A. Ramos and D 68, 094014 (2003) [arXiv:hep-ph/0306146]. U. G. Meissner, Nucl. Phys. A 725, 181 (2003) [94] P. Bicudo, M. Faria, G. M. Marques and J. E. Ribeiro, [arXiv:nucl-th/0303062]. Nucl. Phys. A 735, 138 (2004) [arXiv:nucl-th/0106071]; [100] E. Oset, A. Ramos and C. Bennhold, Phys. Lett. P. J. A. Bicudo, G. Krein, J. E. F. Ribeiro and J. E. Vil- B 527, 99 (2002) [Erratum-ibid. B 530, 260 (2002)] late, Phys. Rev. D 45, 1673 (1992). [arXiv:nucl-th/0109006]. [95] J. E. Villate, D. S. Liu, J. E. Ribeiro and P. J. de A.Bicudo, Phys. Rev. D 47, 1145 (1993).